Radio frequency transmission line



Oct. 22, 1935. w. VAN B. ROBERTS RADIO FREQUENCY TRANSMISSION LINE Filed June 29, 195

Jl ll INVENTOR WALTER VAN BJKOBERTS BY g/WVW AT ToR NEY Patented Oct. 22, 1935 PATENT OFFICE RADIO FREQUENCY TRANSMHSSION LINE Walter van B. Roberts, Princeton, N. J assignor to Radio Corporation of America, a corporation of Delaware Application June 29, 1932, Serial No. 619,843

14 Claims.

My present invention relates to radio frequency transmission lines, and more particularly to a transmission line for radio frequency currents having distributed constants which vary from point to point along the line.

One of the main objects of the invention is to provide an improved radio frequency transformer. A secondary object of the invention is to provide means for; connecting a source of current of a given internal resistance to a load situated at a considerable distance away, and of diiferent resistance, without the use of transformers other than the connecting line itself.

Another object of the invention may be achieved by the use of a transmission line having series inductance and shunt capacity, provided the amount of capacity and inductance per unit length varies from point to point in suitable fashion.

The novel features which I believe to be characteristic of my invention are set forth in particularity in the appended claims, the invention itself, however, as to both its organization and method of operation will best be understood by reference to the following description taken in connection with the drawing in which I have indicated diagrammatically several circuit arrangements whereby my invention may be carried into effect.

In the drawing, 7

Fig. 1 shows an analysis of the principle underlying the invention,

Fig. 2 shows an embodiment of the invention,

Fig. 3 shows still another form of the invention,

Fig. 4 shows another embodiment of the invention.

The reactions and interactions taking place in the structure of this invention make it desirable touse mathematical formulae to elucidate the laws governing the phenomena taking place in the structure, and particularly in laying down rules of design whereby any one skilled in the art may construct the embodiments of the invention.

In the analysis that follows the inductance and capacity will be considered as smoothly distributed, but it is well known in the art that lumped constants may be used provided that a fairly large number of lumps, for example twelve or more, are used per wave length of the current to be handled.

Referring to Fig. 1 let V represent the voltage across the line I, 2, and i the current in the line. Also let Z and g respectively represent the series impedance per unit length of the line and the shunt admittance per unit length. Then, the fundamental differential equations of the line are- By differentiating Equation 1 with respect to x we have:

Now, substitute in Equation 3 the value of l dx 1 given by Equation 2 and the value of 2 given by Equation 1, and we have where a is a constant and Z0 equals the series 80 impedance per unit length of line at the position m=0. Using these values of Z and a in Equation 4 we have:

To solve this equation substitute V=e and we obtain the equation:

m +2amZ g =0 Calling m1 and ma the two values of m which satisfy Equation 8 we have:

(9) V: Ae'" +Be"" where A and B are arbitrary constants. From Equation 9, by means of Equation 1 we also have:

E1 m s .9.3 m z (10) 1- Ae 1 Be I 50 In order to evaluate the two arbitrary constants let the line be terminated at zr=l by an impedance R, and let the voltage applied at r=0 be E. Then, we have, at 23:0, V=E, while at x=l, V=iR. Applying these conditions to Equa- 5 According to the construction of the line we have six cases to consider even if for simplicity the line is assumed dissipationless, that is, Zogo is real and negative:

and t' d R R a on posi lve an 5 10 A m l 1!: Z: m l m l (V a) e l I zzmlAe 1, z I 03 l oEOI- whence In this case both 1121 and 1122 are real andnegative,

, V e (1+m )E e" 1+ )E 10 (10b) A Z l and using these values of A and B in Equation 10 We finally have s a and since Z0 is assumed to be a pure'inductive m z 1 1) 1 Now, the input impedance, E/io is easily obtained from Equation 11 by setting 112:0, and is The problem to be taken up, now that Equation 12 has beenobtained, is this: Can afunction of Z be discovered which, when substituted for R, makes the input impedance independent of Z, subject to the further condition that the phase angle of impedance R is constant and always the same as the phase angle of the input impedance? Ifsuch a value of R is used to terminate the line, the line will act as an ideal transformer as it will alter only the absolute magnitude of R.

I have determined that the above requirements can be met by making For if we substitute 7 Equation 12 we find that V 7 Elm 1 n 1! and since 7 Z =Z e' we may rewrite V Z0v Terminating impedance= e 3 l I t d (1 npu lmpe ance H m1 Impedance ratio =e Similarly, if m2 is used instead of mi equations result identical with Equation 13, except for changing the subscripts of the ms.

The next step is to replace m1 and 1712 by their will be pure inductive'reactances also;

(1)) a negative but o o| In this case both m1 and me are real and positive, 2 so that the line may be terminated by a con densive reactance;

(c) on positive and (e) a positive and a IZ g In this case m1 is a complex in the second quadrant, while m is a complex lying in the third 0;.

quadrant. However l 1I=l 2l-=lw 2El so we may write 1 [1/ TQO and 7 and the terminating impedance will be either In this case conditions are the same as in the previous one except that 0: becomes an expanding factor, and 01 falls in the first quadrant while H2 is in the fourth quadrant. V

A study of these six special cases reveals that in the last four the input impedance of a line 5 terminated in accordance with the invention has an absolute value Z 80 and is independent of the value of a. As a is increased from zero up to the critical value the terminating and input impedances change from pure resistance to pure reactanoe, the sign of the reactance depending upon the sign of a. (If on is positive, the reactance is positive and vice versa). If a is increased beyond the critical value the input and terminating impedances remain pure reactances. It will be noticed that the load or terminating impedance may be kept nearly pure resistanceby keepingsmall, while the ratio of impedances may nevertheless at the same time be made great by using a large value of Z, the length of the line.

In its preferred form howeverthe invention is practised by utilizing a line whose length is an integral number of half wave lengths. For in this case, e =e and Equation 12 then becomes al (15) Re i x R ,=R e log j where L and C are the inductance and capacity onunit length of line. The impedance tapering characteristic 2 on is, obviously, given by the quantity constructed that gR /R In Equation no limitation is put upon the phase angle of R so that a length of line which is an exact number of half "wave lengths acts like an ideal transformer of voltage ratio e and this action is independent of the actual value of line impedance, depending only on the rate of tapering of the line impedance which is determined by the value of 2 0:. This last feature is important in practice.

For example, it is known that a quarter wave length of uniform line (i. e., a=0) will act as an ideal transformer to connect a generator of internal resistance T1 to a load resistance 1'2 provided the characteristic impedance of the line is made equal to However in case turns out to be much larger than about 1000 ohms,

or much smaller than about 300 ohms a simple two wire transmission wire would have to have its wires spaced impracticably far apart or near together to obtain the required characteristic impedance, or else, artificial loading, either capacitive or inductive, would be required.

According to this invention, however, the most convenient spacing may be chosen for an intermediate part of the line, with the result that at no part of the line does the spacing become either impracticably close or far apart. Of course, if a very large ratio of transformation is required, a

large variation of spacing would occur if a single line were used, but in such cases the transformation would be made in a number of sections, each for example one-half wave length long, and each having variable spacing between the wires, as shown which never departs far from the most convenient value.

Such an arrangement is shown in Fig. 2, where a resistance R1 of say 10,000 ohms is shown as a load for a screen grid vacuum tube 3, connection being made through three half wave sections of transmission line 4, 5 designed according to the invention to give impedance ratios of 3:1 per section. Thus, the vacuum tube is working into an impedance of 270,000 ohms which is a reasonable value for a screen grid tube. To achieve the same results with a uniform quarter wave line would require its characteristic impedance to be ohms which in turn would require impracticably great spacing of open wires, or else expensive loading inductance.

In Fig. 3 is shown a modification of the invention, wherein the output tube 6 of a transmitter is directly connected to an antenna 1 of 100 ohms radiation resistance by the tapered line 8, 9. Thus, the line 8, 9 may be used without the necessity for any transformer for feeding maximum power into the load (1) from the source 6 having a higher internal resistance.

In Fig. 4 is shown still another modification wherein the tapered line 8', 9' is used to couple the output of screen grid tube 29 to the primary 2| of the transformer M. The secondary 22 of the transformer M is tuned by the variabletuning condenser 23, and an amplifier 24 may be inter posed between the load and the tuned circuit 22, 23. The line is here used to give the best efficiency at the lowest frequency of a desired operating range as determined by the maximum and minimum values of condenser 23.

The desired taper of the line may be easily secured as indicated diagrammatically in Figs. 2, 3, and 4 by properly spacing the two wires of a .transmission line, or two wire conductor at variable distances apart. 'The proper distance to secure the desired impedance at the several points along the line may be easily determined from the known Formula (16) characteristic impedance 2D 276 log where D is the distance between wire centers and d is the diameter of the wire used.

While-I have indicated and described several systems for carrying my invention into effect, it will be apparent to one skilled in the art that my invention is by no means limited to the particular organizations shown and described,'but

that many modifications may be made without departing from the scope o1v my invention as set forth in the appended claims.

What I claim is:

1. A radio frequency impedance matching device having terminals adapted to be connected to loads of different impedances comprising a pair of conductors, whose length is an exact number of half Wave lengths, the impedance of said matching device tapering in an exponential manner substantially continuously along the length of said conductors whereby its terminals present impedances having values which areequal to the impedances to be matched.

2. In combination, a source of current of a given internal resistance, a load situated at a considerable distance away and having a different resistin length and includinga pair of conductors varying exponentially in impedance along the section length. I

4. An aperiodic electrical impedance transformer comprising a line including a plurality of identical sections, the inductances and capaciponentially, there being an exact number of half wave length sections in the line;

5. In combination, a screen grid tube having a source of energy coupled to its input circuit and an output circuit having a relatively high impedance, a load substantially resistive at the operating frequency to be connected to said output circuit, and having a relatively low impedance, and a couplingmeans between said load and said output circuit comprising one or more half wave sections, each section comprising a pair of conductors tapered to give an exponentially varying impedance. 7 V

6. A combined transmission line and transformer for connecting a pair of terminals to an absorbing device of impedance R2 in such fashion that at the operating frequency the impedance measured between said terminals is R1 which comprises a transmission line whose electrical length at the operating frequency is an exact multiple of a half wave length, and whose series inductance L per unit length is so related to its shunt capacity C per unit length that the quantity at any point on the line distant a: from the ter- "minals is given by the expression I V X R3 I R e log wherein Z is the total length of the line and. e is the Naperian base of logarithms.

' 7. A tapered transmission line having series inductive impedance Z per unit length and shunt condensive admittance g per unit length, Z and g where Z0 and go are the values of Z andg when x=0, a is a constant real quantity and eis the Naperian base of logarithms.

8. The combination of the transmission line defined in the preceding claim and a terminating impedance connected across said line, said terminating impedance having a value equal to r where Z denotes the length of the line and .9. A transmission line of the type defined in claim 7 and in which a has a positive value of such magnitude that a Zogo, in combination with a load connected across the terminals of. said line, said load consisting of a substantially pure inductance.

-10. A transmission line of the type defined in claim 7 and in which a has a negative value of such magnitude that a Zog0, in combination with a load connected across the terminals of said line, said load consisting substantially entirely of capacity reactance.

11. A transmission line of the type defined in claim 7 and in which 0: has a positive value of such magnitude that a =Z0g0, in combination with a load connected across the end of said 1ine said load having an inductive reactance value'of where 2 denotes the length of the line.

13. A transmission line of the type deflned'in claim '7 and in which or has such a value that a Zogo, in combination with a load connected across the terminals of. said line, said load consisting substantially entirely of a resistance.

14. In combination, a circuit tunable through arange of frequencies comprising a'coil and a variable condenser, a tapered transmission line,

means for impressing radio frequency voltages across one end of said line and means coupling the other end of said line to said tunable circuit, the taper 01' said line being so arranged that it operates with highest efiiciency at the end of said frequency range where the power factor of the tunable circuit is poorest, thereby making the voltage developed across the coil of said tuned circuit more uniform as said condenser'is ad-' justed to tune said circuit.

WALTER Wm B. ROBERTS. 

